Multiple sparse Bayesian learningAny MMV algorithm can be used to recover joint-sparse columns of \(\mathbf {Z}_t^k\) , but we use MSBL due to its high performance.
MSBL also outputs a "plug-in" MMSE channel estimate which can then be used to find a meaningful SINR expression since the estimate is uncorrelated with the estimation error [1]}.
(MSBL) [2]} is an empirical Bayesian algorithm that can recover \(\mathbf {Z}_t^k\)  from linear under-determined observations \(\overline{\mathbf {Y}}_t^{pk} \) .
In MSBL, a Gaussian prior is imposed on the columns of \(\mathbf {Z}_t^k\)  as
\(p(\mathbf {Z}_t^k; \! \mathbf {\gamma }_{kt} ) \! = \! \textstyle {\prod \nolimits _{n=1}^N} p([\mathbf {Z}_t^k]_{:,n}; \! \mathbf {\gamma }_{kt}) \! = \! \textstyle {\prod \nolimits _{n=1}^N} \mathcal {CN}(\mathbf {0}_{M_t}, \mathbf {\Gamma }_{kt}), \! \) 
